Why privilege the center of mass as the reference point? Do we need to find the densest concentration of mass in the known universe to determine what we call the punctum fixum and what we call the punctum mobile?
As far as I can tell, most of the local universe revolves around me. That may be a common human misconception, seeing as I’m not a black hole, if we only go by centers of mass. But do we have to?
(Also, “densest concentration of mass” would probably be in the bible belt.)
I think the center of mass thing is a bit of a red herring here. While velocity and position are all relative, rotation is absolute. You can determine if you’re spinning without reference to the outside world. For example, imagine a space station you spin for “gravity”. You can tell how fast it’s spinning without looking outside by measuring how much gravity there is.
You can work in earth-stationary coordinates, there will just be some annoying odd terms in your math as a result (it’s a non-inertial reference frame).
You can determine if you’re spinning without reference to the outside world.
Technically, no you can’t. Per EY’s points on Mach’s principle, spinning yourself around (with the resulting apparent movement of stars and feeling of centrifugal stresses) is observationally equivalent to the rest of the universe conspiring to rotate around you oppositely.
Einstein’s theory further had the property that moving matter would generate gravitational waves, propagating curvatures. Einstein suspected that if the whole universe was rotating around you while you stood still, you would feel a centrifugal force from the incoming gravitational waves, corresponding exactly to the centripetal force of spinning your arms while the universe stood still around you.
The c.g. of the earth/sun solar system would likewise lack a privileged position in such a world.
You can determine if you’re spinning without reference to the outside world.
Technically, no you can’t.
Is that correct? Spinning implies rotation implies acceleration, which I’d always thought could be detected without external reference points.
Per EY’s points on Mach’s principle, spinning yourself around (with the resulting apparent movement of stars and feeling of centrifugal stresses) is observationally equivalent to the rest of the universe conspiring to rotate around you oppositely.
Without taking a stance on Mach’s principle or that specific question of observational equivalence, what about a spinning body in an otherwise empty universe? As an extreme example, my own body could spin only so fast before tearing itself apart. Surely this holds even if I’m floating in an otherwise utterly empty universe?
Is that correct? Spinning implies rotation implies acceleration, which I’d always thought could be detected without external reference points.
This is addressed later in the article, very well IMHO. Let me just give the relevant excerpts:
If you tried to visualize [the entire universe moving together], it seems like you can imagine it. If the universe is standing still, then you imagine a little swirly cloud of galaxies standing still. If the whole universe is moving left, then you imagine the little swirly cloud moving left across your field of vision until it passes out of sight.
But then, … you can’t always trust your imagination. [...]
Suppose that you pick an arbitrary but uniform (x, y, z, t) coordinate system. [… Y]ou might say:
“Since there’s no way of figuring out where the origin is by looking at the laws of physics, the origin must not really exist! There is no (0, 0, 0, 0) point floating out in space somewhere!”
Which is to say: There is just no fact of the matter as to where the origin “really” is. [...]
[...]
And now—it seems—we understand how we have been misled, by trying to visualize “the whole universe moving left”, … The seeming absolute background, the origin relative to which the universe was moving, was in the underlying neurology we used to visualize it!
I worry I’m missing something obvious, but that EY quote doesn’t seem to address my belief (namely, that detecting accleration doesn’t need an external reference point). It just argues there’s no absolute origin to use as an external reference point.
Einstein suspected that if the whole universe was rotating around you while
you stood still, you would feel a centrifugal force from the incoming
gravitational waves, corresponding exactly to the centripetal force of
spinning your arms while the universe stood still around you. So you could
construct the laws of physics in an accelerating or even rotating frame of
reference, and end up observing the same laws—again freeing us of the
specter of absolute space.
(I do not think this has been verified exactly [emphasis arundelo’s],
in terms of how much matter is out there, what kind of gravitational wave it
would generate by rotating around us, et cetera. Einstein did verify that a
shell of matter, spinning around a central point, ought to generate a
gravitational equivalent of the Coriolis force that would e.g. cause a
pendulum to precess. [Wow!] Remember that, by the basic principle of
gravity as curved spacetime, this is indistinguishable in principle from a
rotating inertial reference frame.)
Edit: You are correct from a classical physics standpoint that if you are
in a windowless room on a merry-go-round, you can tell whether the
merry-go-round is standing still versus spinning at a constant speed. (For
instance, you could shoot a billiard ball and see whether its path is straight
or curved.) This contrasts with the analogous situation in a windowless train
car, where you cannot tell whether the train is standing still versus moving
with a constant velocity.
Right, that (a small portion of it) was what I quoted first, one exchange upthread, and satt still held to the intuition that there are rotational stresses in the absence of the universe’s background matter. So I went back/up/down[1] a level to the basic question of when you can rule out a certain “absolute” in nature: when the simplest laws stop requiring it.
The point I was trying to make (which I should have been more specific on) was that, just as the Galilean observation set sufficed to rule out “special” velocities and leave only relative ones, our observation set now has, as an optimal description, laws that give no privilege to any non-relative motion, including higher derivatives of velocity.
[1] whichever preposition would be least offensive
[EY quote on the covariance of physical law for a spinning body]
Edit: You are correct from a classical physics standpoint that if you are in a windowless room on a merry-go-round, you can tell whether the merry-go-round is standing still versus spinning at a constant speed.
As far as I can tell, what I’m saying holds even for non-spinning accelerating objects, and under quantum physics. According to QFT, a sufficiently sensitive thermometer accelerating through a vacuum detects a higher temperature than a non-accelerating thermometer would. This appears to be a way for a thermometer to tell whether it’s accelerating without having to “look” at distant stars & such.
Hm, I’m not sure the thermometer can conclude that it’s accelerating from seeing the black body radiation. I think it’s equivalent to there being an event horizon behind it emitting hawking radiation (this happens when you accelerate at a constant rate). The thermometer can’t tell if it’s next to a black hole or if it’s accelerating. Could be wrong though, but I vaguely remember something along these lines.
I don’t see anything incorrect in what you say. (Sounds to me like a direct consequence of the equivalence principle, although I’m no GR expert.) But I’m assuming away the possibility of rogue black holes in this hypothetical, since I’m wondering whether a sufficiently sensitive sensor could detect its own acceleration even inside an otherwise empty universe (or at least without reference to the rest of the cosmos).
I think I misunderstood what you and Silas were talking about. (Note though that my train thought experiment was about a train with a constant velocity. The billiard ball technique works to detect acceleration of the train even if no rotation is involved.)
Yes, all acceleration is absolute, not relative. You don’t need hypothetical esoteric effects to detect it, a usual weighing scale will do. Gravity throws a bit of a quirk in it, of course.
I’m simultaneously reassured (that my intuition’s correct) & confused (about SilasBarta & Eliezer’s remarks, since they read to me like they contradict my intuition). Maybe I should post a comment on the Sequences post rather than continuing to press the point here, though.
[Edit: originally linked the wrong Sequences post, fixed that.]
I agree that it’s at least quite plausible (as per your post, it’s not proven to follow from GR) that if the universe spun around you, it might be exactly the same as if you were spinning. However, if there’s no background at all, then I’m pretty sure the predictions of GR are unambiguous. If there’s no preferred rotation, then what do you predict to happen when you spin newton’s bucket at different rates relative to each other?
EDIT: Also, although now I’m getting a bit out of my league, I believe that even in the massive external rotating shell case, the effect is miniscule.
Why privilege the center of mass as the reference point? Do we need to find the densest concentration of mass in the known universe to determine what we call the punctum fixum and what we call the punctum mobile?
As far as I can tell, most of the local universe revolves around me. That may be a common human misconception, seeing as I’m not a black hole, if we only go by centers of mass. But do we have to?
(Also, “densest concentration of mass” would probably be in the bible belt.)
I think the center of mass thing is a bit of a red herring here. While velocity and position are all relative, rotation is absolute. You can determine if you’re spinning without reference to the outside world. For example, imagine a space station you spin for “gravity”. You can tell how fast it’s spinning without looking outside by measuring how much gravity there is.
You can work in earth-stationary coordinates, there will just be some annoying odd terms in your math as a result (it’s a non-inertial reference frame).
Technically, no you can’t. Per EY’s points on Mach’s principle, spinning yourself around (with the resulting apparent movement of stars and feeling of centrifugal stresses) is observationally equivalent to the rest of the universe conspiring to rotate around you oppositely.
The c.g. of the earth/sun solar system would likewise lack a privileged position in such a world.
Is that correct? Spinning implies rotation implies acceleration, which I’d always thought could be detected without external reference points.
Without taking a stance on Mach’s principle or that specific question of observational equivalence, what about a spinning body in an otherwise empty universe? As an extreme example, my own body could spin only so fast before tearing itself apart. Surely this holds even if I’m floating in an otherwise utterly empty universe?
This is addressed later in the article, very well IMHO. Let me just give the relevant excerpts:
I worry I’m missing something obvious, but that EY quote doesn’t seem to address my belief (namely, that detecting accleration doesn’t need an external reference point). It just argues there’s no absolute origin to use as an external reference point.
Silas is talking about this:
Edit: You are correct from a classical physics standpoint that if you are in a windowless room on a merry-go-round, you can tell whether the merry-go-round is standing still versus spinning at a constant speed. (For instance, you could shoot a billiard ball and see whether its path is straight or curved.) This contrasts with the analogous situation in a windowless train car, where you cannot tell whether the train is standing still versus moving with a constant velocity.
Right, that (a small portion of it) was what I quoted first, one exchange upthread, and satt still held to the intuition that there are rotational stresses in the absence of the universe’s background matter. So I went back/up/down[1] a level to the basic question of when you can rule out a certain “absolute” in nature: when the simplest laws stop requiring it.
The point I was trying to make (which I should have been more specific on) was that, just as the Galilean observation set sufficed to rule out “special” velocities and leave only relative ones, our observation set now has, as an optimal description, laws that give no privilege to any non-relative motion, including higher derivatives of velocity.
[1] whichever preposition would be least offensive
Ah, sorry. Upthread reading fail on my part.
As far as I can tell, what I’m saying holds even for non-spinning accelerating objects, and under quantum physics. According to QFT, a sufficiently sensitive thermometer accelerating through a vacuum detects a higher temperature than a non-accelerating thermometer would. This appears to be a way for a thermometer to tell whether it’s accelerating without having to “look” at distant stars & such.
Hm, I’m not sure the thermometer can conclude that it’s accelerating from seeing the black body radiation. I think it’s equivalent to there being an event horizon behind it emitting hawking radiation (this happens when you accelerate at a constant rate). The thermometer can’t tell if it’s next to a black hole or if it’s accelerating. Could be wrong though, but I vaguely remember something along these lines.
I don’t see anything incorrect in what you say. (Sounds to me like a direct consequence of the equivalence principle, although I’m no GR expert.) But I’m assuming away the possibility of rogue black holes in this hypothetical, since I’m wondering whether a sufficiently sensitive sensor could detect its own acceleration even inside an otherwise empty universe (or at least without reference to the rest of the cosmos).
I think I misunderstood what you and Silas were talking about. (Note though that my train thought experiment was about a train with a constant velocity. The billiard ball technique works to detect acceleration of the train even if no rotation is involved.)
Yes, all acceleration is absolute, not relative. You don’t need hypothetical esoteric effects to detect it, a usual weighing scale will do. Gravity throws a bit of a quirk in it, of course.
I’m simultaneously reassured (that my intuition’s correct) & confused (about SilasBarta & Eliezer’s remarks, since they read to me like they contradict my intuition). Maybe I should post a comment on the Sequences post rather than continuing to press the point here, though.
[Edit: originally linked the wrong Sequences post, fixed that.]
I agree that it’s at least quite plausible (as per your post, it’s not proven to follow from GR) that if the universe spun around you, it might be exactly the same as if you were spinning. However, if there’s no background at all, then I’m pretty sure the predictions of GR are unambiguous. If there’s no preferred rotation, then what do you predict to happen when you spin newton’s bucket at different rates relative to each other?
EDIT: Also, although now I’m getting a bit out of my league, I believe that even in the massive external rotating shell case, the effect is miniscule.
EDIT 2: See this comment.
Are you sure you linked the right comment? That’s just someone talking about centripetal vs centrifugal.
No, I didn’t. It’s fixed now, thanks.